Marginal Operators from Celestial Diamonds

TL;DR

The paper develops a framework for exactly marginal deformations in celestial CFTs by organizing primary descendants into celestial diamonds and constructing composite, spin-aware marginal operators from soft modes and their Goldstone/shadow partners. It shows that in gravity single-particle marginals are generically unavailable, so marginals arise from multi-particle composites whose primarity depends on non-singular OPEs, linking these deformations to bulk vacuum transitions. A central proposal is the infinite tower of marginal operators M_n(z, z̄), built from conformally soft modes and their partners, which induce transitions among an infinite set of asymptotically flat vacua and parameterize the celestial CFT conformal manifold. This establishes a precise holographic bridge between bulk vacuum structure and boundary conformal geometry, with concrete OPE and transform structures guiding the construction and interpretation of marginal deformations in gauge theory and gravity.

Abstract

For a given conformal field theory (CFT), one can deform it via the addition of a marginal operator to the spectrum. In two dimensions, when the added operator has conformal weights $h=\bar{h}=1$, conformal symmetry is not broken and the resulting theory is a distinct CFT. Studying such marginal operators for celestial CFTs allows for a geometric understanding of the space of allowed boundary theories dual to quantum field theories (QFT) in bulk asymptotically flat spacetimes. In traditional holographic examples, a marginal deformation on the boundary corresponds to a vacuum transition in the bulk theory. We affirm this in celestial CFTs which requires a general definition of marginal operators as composite celestial operators via pairs that live at distinct corners of celestial memory and Goldstone diamonds.

Figures (4)

• Figure 1.1: The infrared triangle for asymptotic symmetries, as in Strominger:2017zoo. We will concern ourselves with the side that relates memory effects to asymptotic symmetries via vacuum transitions.
• Figure 3.1: We show the pair of diamonds that we are interested in for general labels of spin and dimension. The pair at the top shows the two diamonds for arbitrary $(\Delta,J)$. On the left is the memory diamond, labeled in red, and on the right is the Goldstone diamond, labeled in blue. The corners of the red and blue diamonds are symplectically paired, notated by the arrows. The bottom set of diamonds is for a choice where $(\Delta,J) = (1+s,k-1)$ for the operator at the top corner. In this case, one corner of the memory diamond can be identified as a soft operator of spin $s$ and dimension $k$. The other corners of the diamonds are notated to show their relation to one another as well as to identify them within the operator spectrum of the celestial CFT.
• Figure 3.2: The memory diamond in the case where the soft operators are spin-1. This corresponds to the $s=-1$ case in the bottom figure of \ref{['Fig:diamond']}. $\Delta=1$ for both of the soft operators, we see that they correspond to the same charge, the large gauge charge. A copy of this diamond also exists for photons.
• Figure 3.3: The three distinct memory diamonds when we choose the soft operators to be restricted to gravitons. Once again when $\Delta=1$ both soft operators correspond to the same charge as we found in the gauge theory case. However, when $\Delta=0$ each helicity soft operator now has their separate diamond.